TTL Comm vs SPI

First I have no experience using SPI which is why I'm asking this
question.

I have an app the sends serial messages (Tx only - no Rx) out a BX24
pin to another device using the usual COM3 implementation at 19.2k
baud. The app spends a substantial amount of time doing this. Would it
be faster to use the SPI bus to do this instead? (The other app could
use SPI instead of serial). What is the relative speed of the SPI bus,
ie. 192.k vs. what?